One maintenance issue I have to deal with is the loss of kitchen corner cupboard doors. This is due to the design of the bi-fold cupboard door which has the weight of the second door hanging off hinges on the first standard hinged door. Closed, this system is to two cupboard doors at 90 degrees. This
system always works loose and ends up in missing screws,hinges and/or doors.

How about a downwards telescoping door. The door would be like a topologically radially stretched car aerial. A circle cross section stretched to a rectangle with two half circles at each end bent in the middle 90 degrees.
The door would be soft close sprung with catches at closed, half shelf height and full open. The door material would be powder coated steel or aluminum.

Of course 100 or so mm is needed for fully compacted size so the complicated bottom hinges lower the door to the floor, through toe-kick height. By telescoping down the door to half or full, the hand and body position is ready to take out needed objects and a slight tap to release catch raises the door.

The door can take on any horizontal cross-sectional shape but must allow the repeatable insert reduction, in the vertical, for telescopic action. I would like the bottom to be the smaller section, for cleanliness, but that would be impossible with bottom hinges.

Ultimately this is a cupboard door that is complex, over engineered and difficult to manufacture, ideal to hide a pile of fish bones.

[RayfordSteele] Because of the 90 degree a roll up won't have the physics. Two roll ups might work but opening then requires two door action.

[8th of 7] In most of the cheaper kitchens, hermetically sealed cupboards are not required just splash resistance, helped by the lip of the bench and a way of hiding of possessions.

True, any knock, dirt will reek havoc with the telescoping. Maybe more end clearance and a high viscosity, kitchen friendly, grease or nylon insert could act as a better bearer. Wall thickness and material will be the determining factor in knock resistance.

I'm not sure exactly what [RayfordSteele] was picturing
with his roll-up option, but if it's built like a roll-top desk
or appliance garage [link], but with two separate sections
that split apart as they go around the curve, that could
work. The bottom piece with the handle would be a
continuous L shape since it doesn't need to go around the
corner. The joint on the rest of the pieces would need to
be some kind of zipper-like mechanism so the pieces lock
together when closed to avoid falling out of the track or
requiring a center column, but when they reach the top
and start going around the curve, they split apart.

Maybe even better would be a roll-down door, so if you
want to reach the top shelf, you only have to bend over
far enough to put the door halfway down, rather than
having to reach all the way to the floor any time you
want to open the door at all. That makes it more like the
original idea as well. It would of course require some
mechanism like springs or counterweights to keep it
closed. The door slats could roll down into the toe-kick
area, or the bottom shelf could be slightly raised.

Roller options do cut down space because of the curvature needed to have a good 90 degree slidey turn. A horizontal slide would not be able to half open. A roller door would be simpler and a tried and true mechanism but the other cabinet doors would have to have a unique slatted finish. The Cubyscope probably would have a draw look to it.

// [ ] roll-up option, [ ] with two separate sections that split apart as they go around the curve,
that could work. [ ] The joint on the rest of the pieces would need to be some kind of zipper-like
mechanism so the pieces lock together when closed to avoid falling out of the track or requiring a
center column, but when they reach the top and start going around the curve, they split apart. //

I'm imagining it would would like the [linked] thing.

// Maybe even better would be a roll-down door, so if you want to reach the top shelf, you only have
to bend over far enough to put the door halfway down, rather than having to reach all the way to the
floor any time you want to open the door at all. //

Agreed. You'd end up using the top shelf more that way. With the door opening from the bottom,
you'd end up using the bottom shelf the most, probably, and that would be inconvenient.

// The door slats could roll down into the toe-kick area, or the bottom shelf could be slightly raised.
//

Isn't the bottom shelf raised already, above the toe-kick? My understanding of common floor-mounted
cabinets is that there's an inaccessible volume under the bottom shelf/drawer for this reason. The
slats could go in there. Depending on how deep the cabinet is, they might not need to roll up.

// I think it should be "Cubbyscope", with two "b"s. I keep reading it and thinking it's got something to
do with cubes. //